The paper is organized as follows. In section  we provide concentration inequalities for the hidden layers of a SDNN and for its output. In section  we provide results for the optimal number of layers.
In section 
we apply our results to a stochastic version of the feedforward neural networks with ReLU activation presented in [1]}. Section 
is a discussion.
To make the paper self-contained we provide background on subGaussian random variables and norm-subGaussian random vectors in Appendix , and on martingales and filtrations in Appendix . We prove our results in Appendix .
